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同调代数
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  homological algebra
     Injective modules play an important role in module theory and homological algebra.
     内射模是模论与同调代数理论中重要的模类。
短句来源
     Homological Algebra is an important part of Algebra.
     同调代数是代数学的一个重要分支,它的兴起对群、李代数与结合代数的研究起了非常重要的作用。
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     The present paper describes the basic facts about the ringed space and the modern mathematical methods: sheaf theory, homological algebra. , cohornology and Grothendicck topology, which are not only used in ringed fpace but extensively used in various branches of the modern mathematics.
     本文介绍了赋环空间的基本事实,同时介绍了层、同调代数、上同调、Grothendieck拓扑等现代数学方法,这些方法不仅在赋环空间而且在现代数学的许多分支都是广泛使用的。
短句来源
     Functor of a tensor product is a main tool of the study of the category of mo-dules in the Homological Algebra;
     张量积函子是同调代数中研究模范畴的重要工具。
短句来源
     ln chapter one, he gives a brief introduction to homological algebra , algebraic K-theory and the background of this paper .
     第一章概述了同调代数与代数K—理论的发展历史及现状,并且对本文的研究背景作了简要介绍。 设A是无单位元环,(?)
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  “同调代数”译为未确定词的双语例句
     Notes On Some Problems In Homology Algebra
     关于同调代数中几个问题的注记
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     Morita duality is an important concept in module theory.
     Morita对偶是模论与同调代数理论中又一重要的概念。
短句来源
     THE HOMOLOGICAL ALGEBRAS OF CHAIN COMPLEXES OF BCI-ALGEBRAS
     BCI-代数链复形的同调代数
短句来源
     Studying dimensions is one of the most important parts in homological theory.
     伴随同调理论的形成,它便一直成为同调代数中研究的焦点。
短句来源
     Moreover, we define the P-injective radical of modules and obtain some properties of them.
     最后我们定义了模的P-内射根,得到了P-内射根的一系列的性质。 内射模是模论与同调代数中重要的模类。
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  相似匹配句对
     THE HOMOLOGICAL ALGEBRAS OF CHAIN COMPLEXES OF BCI-ALGEBRAS
     BCI-代数链复形的同调代数
短句来源
     Some Homological Properties of Positive Graded Algebras
     正分次代数上的一些同调性质
短句来源
     FP ALGEBRA
     FP代数
短句来源
     The Representation of Algebra C
     代数C[x,y]的表示
短句来源
     Homological Equations
     同调方程
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  homological algebra
We present a complete mechanized proof of the result in homological algebra known as basic perturbation lemma.
      
That homological algebra finds a place in the study of topological string theory should not surprise the reader, granted that topological string theory is the conformal field theorist's algebraic topology.
      
The absolute cohomology is obtained by an independent method based on homological algebra.
      
Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras.
      
A counterexample to a 1961 "theorem" in homological algebra
      
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The ringed space is a recent development of the geometric function theory. The present paper describes the basic facts about the ringed space and the modern mathematical methods: sheaf theory, homological algebra., cohornology and Grothendicck topology, which are not only used in ringed fpace but extensively used in various branches of the modern mathematics.

赋环空间是几何函数论的最新发展。本文介绍了赋环空间的基本事实,同时介绍了层、同调代数、上同调、Grothendieck拓扑等现代数学方法,这些方法不仅在赋环空间而且在现代数学的许多分支都是广泛使用的。

Functor of a tensor product is a main tool of the study of the category of mo-dules in the Homological Algebra; On the basis of [1], we have discussed the tensorproduct of B-spaces and got some results, in this paper.Let B-spaces E and {E_i, j∈J} be given, then E∪_(E_i()∪_()E()E_. If βand β_i are cross-norm, then E(?)_(?)∪_(i=1)~(?) E_(?) is an isometry with a subspace of ∪_(i=1)~(E_(β_j) E_i). Next. we generalize Adjoint Isomorphism Theory of the HomologicalAlgebra. Let E_1, E_2 and F be B-spaces. then (B_1_...

Functor of a tensor product is a main tool of the study of the category of mo-dules in the Homological Algebra; On the basis of [1], we have discussed the tensorproduct of B-spaces and got some results, in this paper.Let B-spaces E and {E_i, j∈J} be given, then E∪_(E_i()∪_()E()E_. If βand β_i are cross-norm, then E(?)_(?)∪_(i=1)~(?) E_(?) is an isometry with a subspace of ∪_(i=1)~(E_(β_j) E_i). Next. we generalize Adjoint Isomorphism Theory of the HomologicalAlgebra. Let E_1, E_2 and F be B-spaces. then (B_1_ E_2, F)(E_2, (E_1,F)) and (E_1(?)E_2,F)(?)(E_1, (?)(E_2, F)). Finally, let E_i, F_ibe B-spaces, f∈(?)(E_1, F_1), g∈(?)(E_2, F_2), then exists uniquely f(?)g∈(?)(E_1(?)E_2, F_1(?)_(β_2) F_2). Let P={sum from i to f_i (?)g_i}, then P is an isomotry with adense subspace of (?)(E_1, F_1)(?)_(?)(?)(E_2, F_2). Specially, we identity E_1 (?)E_2with a subspace of(E_1(?)_(?) E_2). The sign on this paper is identified with [1]

张量积函子是同调代数中研究模范畴的重要工具。在[1]的基础上,本文对B-空间的张量积做了讨论,得出一些新的结论。设E是B-空间,{E_i,j∈J}是B-空间族,作为赋范空间,则E(?)∪_(i∈J)E_i与∪_(i∈J)(E(?)E_i)等距同构。作为B-空间,E(?)_(?)∪_(i=1)~(?)E_i与∪_(i=1)~(?)(E(?)_(β_(?))E_i)的子空间等距同构。其次本文推广了著名的伴随同构定理([2]Th2.11).设E_1,E_2与F是B-空间,则(?)(E_1(?)_(?)E_2,F)分别与(?)(E_2,(?)(E_1,F)),(?)(E_1,(?)(E_2,F))等距同构.特别(E_1(?)_(?)E_2)分别与(?)(E_2,E_1),(?)(E_1,E_2)等距同构.最后,设E_i,F_i是B-空间,f∈(?)(E_1,F_1),g∈(?)(E_2,F_2),则存在唯一的φ∈(?)(E_1(?)_(β_1)E_2,F_1(?)_(β_2)F_2),记φ=f(?)g.令P={sum from i to f_i(?)g_i},则P与(?)(E_1,F_1)(?)_(?)(...

张量积函子是同调代数中研究模范畴的重要工具。在[1]的基础上,本文对B-空间的张量积做了讨论,得出一些新的结论。设E是B-空间,{E_i,j∈J}是B-空间族,作为赋范空间,则E(?)∪_(i∈J)E_i与∪_(i∈J)(E(?)E_i)等距同构。作为B-空间,E(?)_(?)∪_(i=1)~(?)E_i与∪_(i=1)~(?)(E(?)_(β_(?))E_i)的子空间等距同构。其次本文推广了著名的伴随同构定理([2]Th2.11).设E_1,E_2与F是B-空间,则(?)(E_1(?)_(?)E_2,F)分别与(?)(E_2,(?)(E_1,F)),(?)(E_1,(?)(E_2,F))等距同构.特别(E_1(?)_(?)E_2)分别与(?)(E_2,E_1),(?)(E_1,E_2)等距同构.最后,设E_i,F_i是B-空间,f∈(?)(E_1,F_1),g∈(?)(E_2,F_2),则存在唯一的φ∈(?)(E_1(?)_(β_1)E_2,F_1(?)_(β_2)F_2),记φ=f(?)g.令P={sum from i to f_i(?)g_i},则P与(?)(E_1,F_1)(?)_(?)(?)(E_2,F_2)的稠密子空间(?)(E_1,F_1)(?)(E_2,F_2)等距同构。特别E_1(?)E_2是(E_1(?)_(β_1)E_2)的子空间。本文中的记号同于[1]。文中涉及到张量积的范数都是Cross-范数。

This paper, based on W·V·Vasconcelos' studies, generalized some results of Auslander, Vasconcelos etc and further characterized modules on local rings and semi-local ring and their homological properties. Auslander-Buchsbaum Nagata have proved a famous theorem using homological method, which cannot be proved by other mathematical method yet : Every regular local ring is a UFD. In this paper, it is proved that if A is a indecomposable coherent semilocal ring, and every principal ideal has finite projective...

This paper, based on W·V·Vasconcelos' studies, generalized some results of Auslander, Vasconcelos etc and further characterized modules on local rings and semi-local ring and their homological properties. Auslander-Buchsbaum Nagata have proved a famous theorem using homological method, which cannot be proved by other mathematical method yet : Every regular local ring is a UFD. In this paper, it is proved that if A is a indecomposable coherent semilocal ring, and every principal ideal has finite projective demension, then A is a GCD. by using homological method combined with method in ring theory. This theorem generalized Auslander-Buchsbaum- Nagata theorem in some extent.

本文是在W·V·Vasconcelos研究的基础上,将Auslander,Vasconcelos等人的一些结果进行推广,对局部环和半局部环上的模及其同调性质作了进一步刻划。Auslander-Buchsbaum-Nagata用同调代数的方法证明了用其它方法还无法证明的著名定理:每个正则局部环是唯一分解整环。本文采用同调代数与环论相结合方法证得定理:若A是一个不可分的凝聚半局部环,且每个主理想有有限投射维数,则A是最大公因子整环。从某种意义上讲此定理推广了Auslander-Buchsbaum-Nagata定理的结果。

 
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